Single-molecule biophysics has transformed our understanding of biology, but also of the physics of life. More exotic than simple soft matter, biomatter lives far from thermal equilibrium, covering multiple lengths from the nanoscale of single molecules to up to several orders of magnitude higher in cells, tissues and organisms. Biomolecules are often characterized by underlying instability: multiple metastable free energy states exist, separated by levels of just a few multiples of the thermal energy scale k _B T , where k _B is the Boltzmann constant and T absolute temperature, implying complex inter-conversion kinetics in the relatively hot, wet environment of active biological matter. A key benefit of single-molecule biophysics techniques is their ability to probe heterogeneity of free energy states across a molecular population, too challenging in general for conventional ensemble average approaches. Parallel developments in experimental and computational techniques have catalysed the birth of multiplexed, correlative techniques to tackle previously intractable biological questions. Experimentally, progress has been driven by improvements in sensitivity and speed of detectors, and the stability and efficiency of light sources, probes and microfluidics. We discuss the motivation and requirements for these recent experiments, including the underpinning mathematics. These methods are broadly divided into tools which detect molecules and those which manipulate them. For the former we discuss the progress of super-resolution microscopy, transformative for addressing many longstanding questions in the life sciences, and for the latter we include progress in ‘force spectroscopy’ techniques that mechanically perturb molecules. We also consider in silico progress of single-molecule computational physics, and how simulation and experimentation may be drawn together to give a more complete understanding. Increasingly, combinatorial techniques are now used, including correlative atomic force microscopy and fluorescence imaging, to probe questions closer to native physiological behaviour. We identify the trade-offs, limitations and applications of these techniques, and discuss exciting new directions.

Although not laying claim to being the inventor of the light microscope, Antonj van Leeuwenhoek (1632–1723) was arguably the first person to bring this new technological wonder of the age properly to the attention of natural scientists interested in the study of living things (people we might now term ‘biologists’). He was a Dutch draper with no formal scientific training. From using magnifying glasses to observe threads in cloth, he went on to develop over 500 simple single lens microscopes (Baker & Leeuwenhoek 1739Phil. Trans.41, 503–519. (doi:10.1098/rstl.1739.0085)) which he used to observe many different biological samples. He communicated his finding to the Royal Society in a series of letters (Leeuwenhoek 1800The select works of Antony Van Leeuwenhoek, containing his microscopical discoveries in many of the works of nature, vol. 1) including the one republished in this edition ofOpen Biology. Our review here begins with the work of van Leeuwenhoek before summarizing the key developments over the lastca300 years, which has seen the light microscope evolve from a simple single lens device of van Leeuwenhoek's day into an instrument capable of observing the dynamics of single biological molecules inside living cells, and to tracking every cell nucleus in the development of whole embryos and plants.

We present a single-molecule tool called the CoPro (concentration of proteins) method that uses millisecond imaging with convolution analysis, automated image segmentation and super-resolution localization microscopy to generate robust estimates for protein concentration in different compartments of single living cells, validated using realistic simulations of complex multiple compartment cell types. We demonstrate its utility experimentally on model Escherichia coli bacteria and Saccharomyces cerevisiae budding yeast cells, and use it to address the biological question of how signals are transduced in cells. Cells in all domains of life dynamically sense their environment through signal transduction mechanisms, many involving gene regulation. The glucose sensing mechanism of S. cerevisiae is a model system for studying gene regulatory signal transduction. It uses the multi-copy expression inhibitor of the GAL gene family, Mig1, to repress unwanted genes in the presence of elevated extracellular glucose concentrations. We fluorescently labelled Mig1 molecules with green fluorescent protein (GFP) via chromosomal integration at physiological expression levels in living S. cerevisiae cells, in addition to the RNA polymerase protein Nrd1 with the fluorescent protein reporter mCherry. Using CoPro we make quantitative estimates of Mig1 and Nrd1 protein concentrations in the cytoplasm and nucleus compartments on a cell-by-cell basis under physiological conditions. These estimates indicate a ∼4-fold shift towards higher values in the concentration of diffusive Mig1 in the nucleus if the external glucose concentration is raised, whereas equivalent levels in the cytoplasm shift to smaller values with a relative change an order of magnitude smaller. This compares with Nrd1 which is not involved directly in glucose sensing, and which is almost exclusively localized in the nucleus under high and low external glucose levels. CoPro facilitates time-resolved quantification of protein concentrations in single functional cells, and enables the distributions of concentrations across a cell population to be measured. This could be useful in investigating several cellular processes that are mediated by proteins, especially where changes in protein concentration in a single cell in response to changes in the extracellular chemical environment are subtle and rapid and may be smaller than the variability across a cell population.

Bacteria use subcellular proteinaceous liquid droplets to survive stress.

The replisome is a multiprotein machine that carries out DNA replication. In Escherichia coli, a single pair of replisomes is responsible for duplicating the entire 4.6 Mbp circular chromosome. In vitro studies of reconstituted E. coli replisomes have attributed this remarkable processivity to the high stability of the replisome once assembled on DNA. By examining replisomes in live E. coli with fluorescence microscopy, we found that the Pol III* subassembly frequently disengages from the replisome during DNA synthesis and exchanges with free copies from solution. In contrast, the DnaB helicase associates stably with the replication fork, providing the molecular basis for how the E. coli replisome can maintain high processivity and yet possess the flexibility to bypass obstructions in template DNA. Our data challenges the widely-accepted semi-discontinuous model of chromosomal replication, instead supporting a fully discontinuous mechanism in which synthesis of both leading and lagging strands is frequently interrupted.